Modern Tribology Handbook, Two Volume Set

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A linear, unbranched fluid formulated with this additive was evaluated under boundary lubrication and elastohydrodynamic EHD lubrications. Performance of the base fluid imporved significantly with the incorporation of this additive. Volume 7 , Issue 1. The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.

If the address matches an existing account you will receive an email with instructions to retrieve your username. Journal of Synthetic Lubrication Volume 7, Issue 1. Sashi K. Lois J. The average indentation depth of the aforementioned grooves ranges from 0. Therefore, while modeling the experimental RR, we now consider a combination of tip-induced plastic deformation and sliding. For the deformation within the area of contact, we consider the problem of a static indenter and calculate the indentation depth.

To simplify the complex problem of the elastic—plastic deformation, we consider the static indentation of our tip with the sample and calculate the indentation depth using the Derjaguin, Muller and Toporov DMT model which predicts a deformed contact profile equivalent to the Hertz theory and accounts in addition for the adhesion in elastic contacts The DMT model is accurate in case of stiff materials, small sphere radii and weak long-range adhesion force in line with our experimental setup.

The expression for the contact radius becomes. The height of the deformed contact, i. Modeling of the experimental RR. This combination provides an improved approximation of our model with the experimental RR, however a certain underestimation of the high-force regime remains. In a very simplistic model ignoring the effect of line overlap one would expect to find a direct correlation between the calculated tip-induced indentation depths and the experimental RR. Although both show an increase with the applied force their growth profile is different.

The calculated results of the tip-induced indentation depth are shown in Fig. The indentation depth predicted by the DMT model exceeds the material removed experimentally at low-force and falls behind the RR in the high-force regime. This is due to the fact that the tip-induced material removal is not just a static-indentation but it is the combined result of tip-induced indentation, plastic deformation and trailing. Based on these observations, we can now start to build a more comprehensive model for RR.

Based on previous observations the wear coefficient K is considered dependent on the contact area and friction force In practice, this means that we allow it to vary with the load force. Since we probe the removal rate, that is the removed volume at the end of a single scan, eq. Using this equation we find in the low-force range i.

As a second removal mechanism, in the high force regime we assume that the plastic deformation indentation dominates, with however a modification to account for the line overlap. Hence in this case. Where d describes the plastic deformation per scan induced by the tip acting as an indenting single asperity. Alpha is an important parameter because as shown in Fig. In practice the two mechanisms are acting together while the tip contact is dragged on the surface and the resulting model is combined of two terms:.

In eq. Finally, as refinement to eq.

Modern Tribology Handbook, Two Volume Set - Library

Therefore, we allowed in eqs 3 — 5 this term to be variable with the load force. Obviously its variation needs to be limited to magnitude consistent with its physical nature. As such we have limited its possible fluctuation at 20x the original value, measured in the low force regime where we assume no plastic deformation. It can be easily seen that without this modification i.

On the contrary, Fig. We observe a good agreement between the experimental RR values and our model. The fitting shown in Fig. SiO 2 , Pt and TiN.

Indeed, despite the high wear resistance of diamond, it is legitimate to consider the impact of an intense material removal on the tip apex itself too. In particular, tip blunting and its potential impact on the RR needs to be considered. This can be done by a direct inspection of the tip-apex by SEM after prolonged material removal Fig. Here, the formation of clusters of material debris on the tip body and their accumulation on the edges of the tip are clearly visible.

Thanks to the different electrons emission property of diamond compared to other materials i. When we assume that the portion of the tip-apex which is not covered by residues, was in direct contact with the sample, this result shows that despite the large amount of removed material, the diamond tip-apex can still be used as a sliding contact. Unfortunately, the SEM inspection carried out only after the sliding experiment, does not yield enough information to assess the effect of the potential tip blunting on the RR.

As discussed in the previous sections, the RR is strongly affected by the tip-sample contact area and therefore also by the tip-apex. Hence one expects that when the load force is kept constant, the RR stays constant over time, provided that the geometry of the tip-apex does not change during the scan. Therefore, some dedicated experiments aimed at monitoring the RR over the number of scans can indirectly be used to study potential changes in the tip-apex. This is presented in Fig. A decreasing trend in the RR as function of repeated scans same force and scan size is shown in Fig. One can consider this effect as the result of the tip-apex becoming blunter leading to a reduced RR.

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This effect reduces the effective RR as the tip is now scanning over the previously removed material, and the result is a false decrease in the RR as in Fig. The latter represents an artifact introduced by the scanning conditions, i.

This can easily be demonstrated, as we show in Fig. Here, the same methodology is used, however this time the scan size is progressively reduced over cycles inset Fig. Excluding the cases of severe tip-apex ruptures or contaminations, repeated experiments such as these indicate a limited impact of the material removal on the physical changes of the tip-apex and thus the RR. This effect, is also not surprising in view of the constant material transport at the trailing end occurring at the edge of the sliding contact.

Introduction to Tribology

Hence, our results indicate that a major showstopper for a constant RR and ultra-precise control of the removal rate is the progressive re-deposition of materials when scanning at a fixed scan size. We observe that this has a major effect on the effective removal capability of the tips. It is worth mentioning that in view of the high precision required by our removal, the range of load-forces is also relatively small which combined with the hardness of the diamond crystallites constituting the apex explain the limited impact on the tip integrity. Impact of the tip-apex contamination and material re-deposition.

Thanks to the high secondary-electron emission for diamond, the area of the tip-apex used in contact with the sample is clearly revealed. In summary, we have demonstrated that the mechanisms of mesoscale material removal established for a sliding AFM tip in contact with the sample surface, can be described by the combination of tip-induced indentation, plastic deformation and material trailing.

Modern Tribology Handbook Two Volume by Bharat Bhushan

Based on the experimental evidences observed by AFM and SEM in the machined areas, we could introduce a model that provides an accurate fit for the experimental removal rate RR in different materials such as metals, oxides and semiconductors. Although the non-linear RR at the transition between an elastic and a plastic surface deformation imposes some limitation for the accurate prediction of the RR, we could demonstrate for all materials a sub-3 nm RR which can be applied to further develop AFM-based tomographic techniques.

In addition, our work clearly indicates the major role of the scan line density on RR, as well as on the quality of the treated surface, both impacting on the final 3D information. The scan frequency determining the scan speed in all the experiments is 0. The deflection sensitivity of the tip under study was measured before, during and at the end of the removal process to assess a possible unrecoverable bending of the cantilever. The machined areas and the contamination of the tip apex were inspected by scanning electron microscopy SEM with a SU Hitachi, Japan system.

Modern Tribology Handbook, Two Volume Set

The experiments were carried out by U. While T.

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All authors have given approval to the final version of the manuscript. Electronic supplementary material. Supplementary information accompanies this paper at Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. National Center for Biotechnology Information , U. Sci Rep. Published online Feb Nordling , 2 Josephus G. Buijnsters , 3 Thomas Hantschel , 1 and Wilfried Vandervorst 1, 4.

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Josephus G. Author information Article notes Copyright and License information Disclaimer. Umberto Celano, Email: eb. Corresponding author. Received Oct 5; Accepted Jan This article has been cited by other articles in PMC. Hamrock Tribology for scientists and engineers : from basics to advanced concepts by Pradeep L. Volume 5 by K. Mittal Lubrication in Practice by W.